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Chapter 4: Problem 242

In the following exercises, simplify. $$\frac{2+4(3)}{-3-2^{2}}$$

Short Answer

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Step by step solution

01

Simplify the Numerator

First, simplify the numerator: \[\begin{equation} 2 + 4(3) \ = 2 + 12 \ = 14 \end{equation}\]
02

Simplify the Denominator

Next, simplify the denominator: \[\begin{equation} -3 - 2^{2} \ = -3 - 4 \ = -7 \end{equation}\]
03

Form the Fraction

Combine the simplified numerator and denominator: \[\begin{equation} \frac{14}{-7} \ = -2 \end{equation}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator Simplification
The numerator is the top part of a fraction. To simplify it, follow these steps:

First, identify any operations that need to be done. In our exercise, the numerator is \(2 + 4(3)\).

Begin by simplifying the expression inside the parentheses. Multiply 4 by 3: \[4(3) = 12 \]

Next, add this result to 2: \[2 + 12 = 14\].

Thus, the simplified numerator is 14. Always remember:
  • Simplify operations inside parentheses first.
  • Perform multiplication and division before addition and subtraction.
Denominator Simplification
The denominator is the bottom part of a fraction. To simplify it, follow these steps:

Identify any operations that need to be done. In our exercise, the denominator is \(-3 - 2^2\).

Start by simplifying the exponent. Calculate \2^2\, which is 4.

Next, subtract this result from -3: \(-3 - 4 = -7\).

Now, the simplified denominator is -7. Key points to remember:
  • Calculate exponents before moving to other operations.
  • Follow the order of operations: parentheses, exponents, multiplication/division, and then addition/subtraction.
Fraction Simplification
Once both the numerator and the denominator are simplified, the fraction itself can be simplified. Here's how:

Combine the simplified components. Our exercise results in the fraction \(\frac{14}{-7}\).

Divide the numerator by the denominator to simplify the fraction: \[ \frac{14}{-7} = -2\].

Therefore, the simplified form of the fraction is -2. Important reminders for fraction simplification:
  • Ensure both numerator and denominator are fully simplified before combining.
  • Remember that a negative sign in the denominator can be moved to the numerator or placed in front of the fraction.
  • Simplify the fraction by dividing the numerator by the denominator.
With these steps, you can simplify any fraction easily.

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Most popular questions from this chapter

In the following exercises, subtract. $$\frac{11}{12}-\frac{5}{12}$$

In the following exercises, perform the indicated operations and simplify. $$\frac{y}{10}-\frac{1}{3}$$

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs \(\frac{3}{16}\) yard of print fabric and \(\frac{3}{8}\) yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

In the following exercises, change to equivalent fractions using the given LCD. $$\frac{1}{3} \text { and } \frac{1}{5}, \quad L C D=15$$

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